Molecular dynamics (MD) simulation and first-principles calculation were used to study the heredity characteristics, evolution trend and structural stability of basic clusters during the rapid solidification of Pd₈₂Si₁₈ alloy. The local atomic structures were characterized by the pair distribution function g(r) and the extended cluster-type index method (CTIM). The MD simulations reveal that the number of bi-cap Archimedes anti-prism (BSAP) clusters with CTIM index (10 2/1441 8/1551) is dominant in the amorphous solids rather than three-cap triangular prism(TTP) with CTIM index (9 3/1441 6/1551), which is identified be the most popular basic units in Pd₈₂Si₁₈ alloys analyzed by Voronoi index Relative to other basic clusters, the Si-centered BSAP possesses much larger fraction in the glassy state of Pd₈₂Si₁₈ alloys. Different from the findings in Cu-Zr alloys, the Si-centered BSAP instead of icosahedra has a larger hereditary fraction than any other Kasper clusters. During the solidification, it was found that most of the other Si-centered basic clusters are transferred into BSAP. Via the DFT calculations, it is observed that the Si-centered basic clusters with higher fraction of heredity and possesses lower binding energy. Among of them, BSAP always keeps lower binding energy than any other Si-centered Kasper clusters during the rapid solidification, resulting in its highest structural stability and the largest heredity fraction.